qid int64 1 4.65M | metadata listlengths 3 3 | prompt stringlengths 31 25.8k | chosen stringlengths 17 28.2k | rejected stringlengths 19 40.5k | domain stringclasses 28
values |
|---|---|---|---|---|---|
72,832 | [
"https://electronics.stackexchange.com/questions/72832",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/24837/"
] | Title explains it, is it possible to create a superconductor using negative resistor oscillator / amplifier? As superconductors are conductors with 0 resistance. Isn't an amplifier a superconductor?
Or is what I am asking for wrong? I just need to learn.
| You could, <em>theoretically</em>, make a circuit that <strong>acts like it is a superconducting wire</strong> (or very close, anyways). This would require <em>active electronics</em>, which would take power, and as such it wouldn't be superconducting from the perspective of efficiency.
You really seem like you need t... | <blockquote>
Title explains it,
</blockquote>
not to me
<blockquote>
is it possible to create a superconducter using negative resistor oscillator/amplifier?
</blockquote>
No. A superconductor is passive component that has 0 resistance. There are circuits that behave as a negative resistance, but they are active... | https://electronics.stackexchange.com |
34,630 | [
"https://dsp.stackexchange.com/questions/34630",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/17904/"
] | I'm considering the following simple system model:
$$\mathbf{y}=\mathbf{Hx}+\mathbf{n}\quad\textrm{with}\quad \mathbf{n} \sim \mathcal{CN}(\mathbf{0},\mathbf{I})$$
The resulting MIMO channel capacity for known and constant $\mathbf{H}$ should be:
$$C = \log_2\det\left(\mathbf{I}+\mathbf{HQH}^H\right)$$
where $\math... | The way you generate the covariance matrix is not right. I would either use Matlab's <code>gallery</code>, or generate a random matrix as follows:
<pre><code>A=rand(N)+j*rand(N);
Q=A*A';
</code></pre>
To check if a matrix <code>Q</code> is positive semidefinite, you can look at the eigenvalues and see they are all no... | <pre><code>N=4;
P=6;
H=randn(N,N);
I=eye(N);
cvx_begin
variable Q(N,N)
maximize log_det(I+H*Q*H')
subject to
trace(Q)<=P
Q==hermitian_semidefinite(N)
cvx_end
</code></pre>
| https://dsp.stackexchange.com |
17,756 | [
"https://mechanics.stackexchange.com/questions/17756",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/10905/"
] | I recently purchased a floor jack and a jack stand set and would like to know about their proper usage. I noticed some people use rubber pads for their floor jack and jack stand contact areas - some of them are bought, some make them from hockey pucks, some use wooden blocks (I think I've heard of simply using a towel ... | It partly depends on the car you are using them with - in the photo you've added, the pad on the stand has a slot in - so I'd guess it's being used with a car that has a lip on the sill - that lip would sit in the slot and the top of the pad would be against the sill of the car - thus avoiding damaging the lip.
The m... | This is most readily left up to user preference.
As for me, it depends on what I'm asking the jack stand to do. The rubber pad is there to protect the underside of the vehicle. As you can tell with the jack stand you have shown on the left, the metal top alone concentrates a lot of weight in a small area. The rubber ... | https://mechanics.stackexchange.com |
675,247 | [
"https://physics.stackexchange.com/questions/675247",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/277655/"
] | <blockquote>
If two bodies exert forces on each other, these forces are equal in magnitude and opposite in direction.
</blockquote>
This law is often addressed as the <em>action-reaction principle</em>, though the term "principle" might suggest we're dealing with a postulate. As such, it cannot be derived fro... | As you mentioned, the third law is just a postulate in classical mechanics. As a side note, a professor of mine would disagree with you that the first law is without independent content of the second law (although <span class="math-container">$a=0$</span> when <span class="math-container">$F=0$</span> <em>is</em> a spe... | Newton's Third Law of motion is a direct consequence of the law of <em>conservation of momentum</em>. In this respect, Newton's third law is more fundamental than seems to be implied. If you change the momentum on one object, then some other object must change its momentum (in an opposite direction), so that the tota... | https://physics.stackexchange.com |
175,605 | [
"https://physics.stackexchange.com/questions/175605",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/75502/"
] | <strong>Scenario</strong>
Suppose there exists an advanced technology that can hypothetically transport living humans to study the center of the Earth, as they goes deeper underground most of the Earth's mass would be above them and thus the gravity will seems lighter.
<strong>Question</strong>
Q1. I do not know if ... | Firstly, the gravitational field inside the Earth, decreases with depth.
To a first approximation, you can use the shell theorem for spherically symmetric mass distributions to argue that the gravitational field at some depth is due only to the mass enclosed within a sphere interior to that depth. If we further make t... | Q1. In the case of a uniform spherical distribution you cannot sense anything further away from the center than you are. This is directly derived from Gauss' law for gravity. At the center you do not feel any net gravitational force from earth at all. Think about it this way: earth is pulling you up from all direc... | https://physics.stackexchange.com |
397,396 | [
"https://mathoverflow.net/questions/397396",
"https://mathoverflow.net",
"https://mathoverflow.net/users/122796/"
] | Let <span class="math-container">$A$</span> and <span class="math-container">$B$</span> denote two <em>countably infinite</em> sets of ordinals.
Let <span class="math-container">$W_A$</span> denote the supremum of ordinals <em>writable</em> by Ordinal Turing Machines with the set <span class="math-container">$A$</span>... | The answer is yes. In fact, you can make the difference enormous.
First, let me construct a certain set of ordinals.
<strong>Lemma.</strong> There is a countable set <span class="math-container">$X$</span> of ordinals such that:
<ol>
<li>Every OTM program that halts with <span class="math-container">$X$</span> as input... | Writing an answer because it was suggested/advised. I will assume constructibility for simplicity. Also, I will assume writeable to mean as written in second last paragraph of question. Going through various examples:
<strong>(1)</strong> All elements of <span class="math-container">$A$</span> are countable and all ele... | https://mathoverflow.net |
243,690 | [
"https://physics.stackexchange.com/questions/243690",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/111473/"
] | A question from Appendix Linear algebra
A.3 Matrices
on
page 441
<blockquote>
"If you know what a prticular linear transformation does to a set of basis vectors, you can easily figure out what it does on any vector. For suppose that: $T |e_1\rangle = T_{11}|e_1\rangle+ T_{21}|e_2\rangle+ ... $"
</blockquote>
Hi! I... | <blockquote>
For suppose that: T|e1> = T11|e1>+ T21|e2>+...
</blockquote>
First, recognize that $T_{ij}$ is a <em>component</em> of T on the basis, i.e.
$$T_{ij} = \langle e_i|T|e_j \rangle$$
In words, $T_{ij}$ is the 'amount' of $|e_i\rangle$ in the transformed basis vector $T|e_j\rangle$.
<blockquote>
i apply... | I like to think in concrete visual examples, so I imagine $T$ to be an operator that, say, "Twists" basis vector $ |e_1\rangle$ into a new direction. In addition it stretches it, if not hermitian. So, as you said, it produces a new vector. That vector may have components along any or all of the basis vectors of the sp... | https://physics.stackexchange.com |
559,226 | [
"https://physics.stackexchange.com/questions/559226",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/198035/"
] | In my book about quantum mechanics it state that the time derivative of an arbitrary observable is:
<span class="math-container">$$\frac{d}{dt}\langle A \rangle = \frac{1}{i\hbar} \langle [A,H] \rangle + \bigg{\langle }\frac{dA}{dt} \bigg{\rangle} $$</span>
with <span class="math-container">$H$</span> being the Hamilto... | I think this is a nice question. It ultimately boils down to the following:
<blockquote>
If <span class="math-container">$i\hbar\frac{d}{dt}|\psi\rangle = H|\psi\rangle$</span>, then why does <span class="math-container">$i \hbar\frac{d}{dt}\big(A|\psi\rangle\big) \neq H\big(A|\psi\rangle\big)$</span>, since <span cla... | Well, I think there is a simpler explanation for that.
First, note that we have
<span class="math-container">$$H|\psi\rangle = i\hbar\frac{d}{dt}|\psi\rangle ~~~(1)$$</span>
That is, if Hamiltonian acts on its eigenstates, we would have that equality (This is Schrodinger equation after all, it gives eigenstates (<span ... | https://physics.stackexchange.com |
130,241 | [
"https://physics.stackexchange.com/questions/130241",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/56263/"
] | A rocket is fired vertically and ascends with a constant vertical acceleration of 20 m/s^2 for 1 minute. It's fuel is then all used and it continues as a free particle.
Find the
<ol>
<li>Maximum height reached by the particle</li>
<li>Total time elapsed from the take off till the rocket strikes the earth.</li>
</ol>
... | <blockquote>
First of all does the acceleration include $g$ in it
</blockquote>
The problem can be worded in two different ways:
<ol>
<li>"The position with respect to the ground changes with constant acceleration $20\ \mathrm{m/s^2}$."</li>
<li>"The passengers feel a constant acceleration of $20\ \mathrm{m/s^2}$."... | <blockquote>
First of all does the acceleration include g in it
</blockquote>
When the acceleration is given like that, all influences (forces) causing the acceleration to have that value have been taken into account. In other words, the specified acceleration is <em>the</em> acceleration, there is no need to add o... | https://physics.stackexchange.com |
253,820 | [
"https://stats.stackexchange.com/questions/253820",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/122731/"
] | I have a question on the slope coefficient of OLS compared to that for Quantile Regression, when facing homoscedastic error terms. The population model may look like:
<span class="math-container">$y_i = \beta_0 + \beta_{1}x_i + u_i$</span>
with <span class="math-container">$u_i$</span> being iid error terms. Will the e... | <blockquote>
Will the estimated slope coefficient <span class="math-container">$\beta_1$</span> always be the same for OLS and for QR for different quantiles?
</blockquote>
No, of course not, because the empirical loss function being minimized differs in these different cases (OLS vs. QR for different quantiles).
<bloc... | Generally the answer is yes, at least for Theil's regression, which is a special case of QR. The slope estimator for Theil's regression is an unbiased estimator of the population slope. If all the requirements for OLS are met, then it has 85% relative efficiency. There are certain circumstances where it becomes more... | https://stats.stackexchange.com |
65,376 | [
"https://mathoverflow.net/questions/65376",
"https://mathoverflow.net",
"https://mathoverflow.net/users/2784/"
] | Let $k$ be a finite field. We define $N(d,g)$ to be the number of plane curves $f(x,y)$ defined over $k$ of degree $d$ with (geometric) genus $g$. If $D(d) := (d-1)(d-2)/2$ (the maximum possible genus), I would expect that as $d$ goes to infinity that the proportion of curves of degree $d$ with genus $D(d)$ would go t... | Fix $g$, the genus, and $q$, the order of $k$.
$N(d,g)$ should be $\approx C q^{3d}$, where $C$ is some constant dependent on $q$ and $g$. (Note that my $C$ has absorbed the $q^{-4}$ in Felipe's answer.) There are some nonrigorous details here.
There are finitely many isomorphism classes of pair $(X, L)$ where $X$ is ... | The set of singular curves of degree $d$ contains the curves with $f(0,0)=f_x(0,0)=f_y(0,0)=0$. The chance that each of these values ($f(0,0),\ldots$) is zero is $1/q$ over the field of $q$ elements, so the proportion of such curves among all curves of degree $d$ is $1/q^3$, hence the proportion of smooth curves is at ... | https://mathoverflow.net |
205,877 | [
"https://softwareengineering.stackexchange.com/questions/205877",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/97554/"
] | It always happen to me that if I leave the stuff for 1-2 months I forget the stuff.
5 months back I had symfony project and I did that. At that time I was very much confident that I can do any project in symfony2.
Then we got one Python project in django and I worked full time on that for few months.
But now when I ... | You only need to keep studying another language should you be required not to adjust your thinking when switching to that language. If you don't need to work in language X next week, then why waste time reading about it? Focus on what you're doing in the <em>now</em>.
For example;
I have to work on two projects const... | If you forget after only 1-2 months, you didn't really know it.
As a programmer progresses, you start learning less about syntax, and more about <strong>concepts</strong>. Even if you switch languages, you're often using the same sort of concepts. Since you're constantly using the concepts, they're harder to forget. S... | https://softwareengineering.stackexchange.com |
672,697 | [
"https://physics.stackexchange.com/questions/672697",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/317059/"
] | If
<span class="math-container">$$
T=
\left[
\begin{array}{cccc}
e^{\beta J} & e^{-\beta J} \\
e^{-\beta J} & e^{\beta J} \\
\end{array} \right]
$$</span>
and
<span class="math-container">$$Z = \sum_{S_i=\pm 1} ... \sum_{S_N=\pm 1} \exp{\beta J(\vec{S_1}\vec{S_2}+\vec{S_2}\vec{S_3}+...+\vec{S_{N-1}}\vec{... | <blockquote>
Then why can we say that:
</blockquote>
Because, each <span class="math-container">$S_i$</span> can only take on two values: +1 or -1
For example, if <span class="math-container">$S_1 = +1$</span> and <span class="math-container">$S_2 = +1$</span> then the <span class="math-container">$e^{\beta J S1S2}$</s... | <span class="math-container">$\newcommand{\e}{\boldsymbol=}$</span>
<span class="math-container">$\newcommand{\p}{\boldsymbol+}$</span>
<span class="math-container">$\newcommand{\m}{\boldsymbol-}$</span>
<span class="math-container">$\newcommand{\gr}{\boldsymbol>}$</span>
<span class="math-container">$\newcommand{\l... | https://physics.stackexchange.com |
577,015 | [
"https://stats.stackexchange.com/questions/577015",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/152952/"
] | I'm comparing the AIC of these two models.
Tensor Product Smooth vs. Thin Plate Spline both fit using <strong>REML</strong>
<pre><code>library(mgcv)
ThinPlateSpline <- gam(Z ~ s(X1, X2, bs="tp", k = 17), data = DF, method="REML")
TensorProductSmooth <- gam(Z ~ te(X1, X2, k = 6), data = DF, ... | AIC is valid for my question. It's confirmed in the book:
<strong>Generalized Additive Models: An Introduction with R (SECOND EDITION), by Simon Wood</strong>
<strong>BRAIN IMAGING EXAMPLE:</strong>
<pre><code>m2 <- gam(medFPQ~s(Y,X,k=100),data=brain,family=Gamma(link=log))
tm <- gam(medFPQ~te(Y,X,k=10),data=brai... | In theory AIC does not require the models to be from the same family. So you can compare models with different forms.
But in practice some implementations omit constants from the likelihood function as they're not necessary for comparison of models from the same family (for example two linear regressions). This can cau... | https://stats.stackexchange.com |
2,481 | [
"https://mechanics.stackexchange.com/questions/2481",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/1298/"
] | All cars I've encountered (here in the UK) have the brake pedal higher than the accelerator pedal.
Is this a standard, world wide?
I would have thought that for safety (getting to it quicker) you'd want the brake lower than the accelerator, so why is it set up the way it is?
Maybe a mechanical reason? Maybe to give ... | None of my cars have the brake higher than the accelerator - they were almost exactly aligned when I bought them - so it may just be a feature of the cars you have driven.
There don't seem to be standards on this, or on spacing of pedals (I my brake and accelerator close together to make heel and toe-ing smoother. In ... | Brake pedals are higher to prevent accidental accelerator depression when braking. Brake pedals should be adjusted up as the braking material wears away.
| https://mechanics.stackexchange.com |
87,816 | [
"https://math.stackexchange.com/questions/87816",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/14829/"
] | Let $f(x)$ be a monotonic increasing function on $[0,\infty)$ and for every $x>0$ it is integrable in $[0,x]$, so that $\lim_{x\to \infty}\frac{1}{x}\int_{0}^{x}f(t)dt=a$. I need to prove that $\lim_{x\to \infty}f(x)=a$.
I tried to use the limit definition:
$|\frac{1}{x}\int_{0}^{x}f(t)dt -a|<\epsilon$ and to u... | Here's a proof sketch:
<ol>
<li>If $f$ is unbounded from above, then show that $\frac1x \int_{0}^{\infty} f(x) ~dx \to +\infty$, as $x \to \infty$ (which, of course, contradicts the hypothesis). This shows that $f$ is bounded above. </li>
<li>Define $b := \sup \{ f(x) \ :\ x \geqslant 0 \}$. (This indeed exists and is... | For increasing $f$:
For $b$ fixed, we have $\lim\limits_{x\rightarrow\infty}{1\over x}\int_0^b f =0$. From this and your hypothesis, we have
$\lim\limits_{x\rightarrow\infty}{1\over x}\int_b^x f =a$.
Now: $$
\tag{1}{f(b)\over x}(x-b)\le {1\over x}\int_b^x f\le {f(x)\over x}(x-b). $$
Taking the limit as $x$ ten... | https://math.stackexchange.com |
39,101 | [
"https://security.stackexchange.com/questions/39101",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/22291/"
] | Today I experienced a situation where a person responsible for the security of a company required a pentesting company to withdraw a clause in the contract that says that:
<em>"during the pentest there exist the possibility to delete or modify sensitive data in the production environment unintentionally due to the ex... | There's no way that a pentester can 100% assure that data will not be modified or deleted, in the same way as they can't assure that system availability won't be affected (I've knocked systems over with a port scan or a single ' character). as you say a web crawler can delete data from a system if it's been set-up bad... | A pentester who claims that he will <em>never</em> alter production data is either a <em>filthy liar</em>, or thinks himself to be a lot more competent than he really is, or strongly intends to do nothing at all (that's the only surefire way of never breaking anything). In any case, you don't want to work with that guy... | https://security.stackexchange.com |
571,991 | [
"https://physics.stackexchange.com/questions/571991",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/271863/"
] | Suppose we have a grounded conducing sphere <em>S</em> and a point charge <em>q</em> outside at a given distance.
My objective is to find the induced charge on the sphere.
My attempt is the following: since the sphere is a grounded conductor, the potential is zero in any point inside and on the surface of the sphere. F... | If a quantum system admits a Lie symmetry group, this means that there exist a unitary strongly continuous representation of that Lie group acting in the Hilbert space of the system. The one-parameter subgroups are represented by one-parameter strongly continuous unitary (sub) groups. Stone's theorem proves that each s... | Physical symmetries are in particular a certain transformation of the system. Translations displace the system from a point to another point. Rotations rotate the system. In general, in order to make sense of this statement one needs to give a prescription for the way that this transformation acts on your description o... | https://physics.stackexchange.com |
109,392 | [
"https://cs.stackexchange.com/questions/109392",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/100853/"
] | I have written the following C code which purpose it is to flip an <strong>unsigned</strong> number in binary representation and give back an <strong>unsigned</strong> number:
<pre><code>long flippingBits(long n) {
return (unsigned)(~n);
}
int main(){
long a = flippingBits(someNumber);
...
}
</code></pre>... | Casting of primitive datatypes works in a very simple way:
<blockquote>
Under the hood, values don't have types. Casting does absolutely nothing.
</blockquote>
As a simple example, let us consider casting 65 to an ASCII character, thus obtaining the symbol <code>A</code>. What happens under the hood? Absolutely not... | <blockquote>
How does the casting of primitive datatypes works?
</blockquote>
The restriction "primitive datatype" is not enough:
Casting from a 16-bit integer to a 32-bit integer works differently than casting between integer types of the same size. And casting between integer and floating-point types is even more... | https://cs.stackexchange.com |
63,602 | [
"https://mathoverflow.net/questions/63602",
"https://mathoverflow.net",
"https://mathoverflow.net/users/2191/"
] | How do people call an additive functor from a triangulated category $C$ to an abelian one that converts distinguished triangles into long exact sequences. Does one usually call a covariant functor of this sort 'homology' and denote it by $H_i$, whereas a contravariant functor is called cohomology and is denoted by $H... | (CW because it's more an over-long comment than a real answer.)
I think there are too many competing normalizations to make a good choice. In lieu of sensible default, call one of them homology, and call the other cohomology and I'm sure it'll be fine. This is also probably why someone worked out the language "left-... | I would say that a cohomological chain complex has cohomology, and that a homological chain complex has homology...
| https://mathoverflow.net |
45,083 | [
"https://datascience.stackexchange.com/questions/45083",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/66759/"
] | Hi I'd like to turn each non zero value of my selected columns to a 1 using mutate_at()
<pre><code> BRAND MEDIA_TYPE INV1 INV2
<chr> <chr> <dbl> <dbl>
b1 newspapers 2 27
b1 magazines 3 0
b2 newspapers 0 0
b3 tv ... | <pre><code>mutate_at(my_data, vars(starts_with("INV")), sign)
</code></pre>
Although I see your INV1 column is a date? I'm not sure how much that'll affect things..
| An alternative approach in case you not have column that starts_with some name a practical approach is doing this:
<pre><code>df %>% mutate(INV1 = INV1/INV1, INV2 = INV2/INV2) %>%
replace(is.na(.), 0)
df = tibble(
`BRAND` = c('b1','b1','b2','b3','b4','b5','b1','b2'),
`MEDIA_TYPE` = c(... | https://datascience.stackexchange.com |
568,412 | [
"https://physics.stackexchange.com/questions/568412",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/260726/"
] | My teachers use <span class="math-container">$B$</span> for representing magnetic field and the standard textbooks do so as well, but recently, one of my friends said that <span class="math-container">$B$</span> is magnetic flux density, and <span class="math-container">$H$</span> is used to represent magnetic field.
I... | They're the same until you need them to be the same, at which point you discover they are slightly different. H is "the magnetic field," while B is "the magnetic induction." However it's quite common to see B referred to as "the magnetic field" as well, because they are so similar.
H is w... | Rob's answer is correct, but it contains only half of the story.
If the only difference between <span class="math-container">$B$</span> and <span class="math-container">$H$</span> field would be a factor <span class="math-container">$\mu$</span> or <span class="math-container">$\mu_0$</span>, or the role played in the ... | https://physics.stackexchange.com |
1,264,259 | [
"https://math.stackexchange.com/questions/1264259",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/223129/"
] | <blockquote>
Calculate without a calculator:
$\left (14^{2014} \right )^{2014} \mod 60$
</blockquote>
I was trying to solve this with Euler's Theorem, but it turned out that the gcd of a and m wasn't 1.
This was my solution so far (also doesn't really work without a calculator):
Prime factorization of 60:<br... | $$X=\large (14^{2014})^{2014}=14^{2014^2}$$
Now, $60=3\times 4\times 5$. Now,
$$X\equiv\begin{cases}(-1)^{2014^2}\equiv 1\pmod3\\ (-1)^{2014^2}\equiv 1\pmod5\\ 7^{2014^2}\cdot 4^{(2014^2)/2}\equiv 0\pmod4\end{cases}$$
Now, use Chinese Remainder Theorem.
| $$\left (14^{2014} \right )^{2014}=(14^2)^{1007\times2014}\equiv 16^{1007\times2014} \mod 60$$
Next, notice that $16\times 16\equiv 16\pmod{60}$ to conclude $16^n\equiv 16\pmod{60}$ for all integers $n\ge 1$
| https://math.stackexchange.com |
11,330 | [
"https://quantumcomputing.stackexchange.com/questions/11330",
"https://quantumcomputing.stackexchange.com",
"https://quantumcomputing.stackexchange.com/users/8193/"
] | I’m hoping the quantum community here might weigh in with some thoughts on something that is bothering me regarding quantum entanglement…something that seems as big a disagreement in the quantum world as the Copenhagen theory, and it’s possibly directly related.
I’m of the belief that quantum entanglement is natural ... | There is no contradiction. Entanglement indeed is a natural property; it is difficult to keep pure states for a long time, because they tend to interact and get entangled with environment; but it also difficult to obtain a particular entangled state, such as Bell state.
Uncontrolled entanglement is natural, controlled... | I completely agree with kludg's answer. To follow it up:
<blockquote>
entanglement is natural and unavoidable
the entanglement bond is flimsy and easy to break
</blockquote>
These two things are intrinsically linked. Entanglement has a property called <em>monogamy</em>. If particle <span class="math-container">$A$</spa... | https://quantumcomputing.stackexchange.com |
3,053,478 | [
"https://math.stackexchange.com/questions/3053478",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/580242/"
] | Let R be a commutative ring with <span class="math-container">$1 \neq 0$</span>. Let <span class="math-container">$M$</span> be the unique maximal ideal of R. I want to show that <span class="math-container">$x \in M$</span> if and only if <span class="math-container">$1+xr$</span> is invertible for every <span class="... | Suppose that <span class="math-container">$x\in M, $</span> for every <span class="math-container">$r, xr\in M$</span> since <span class="math-container">$M$</span> is an ideal. If <span class="math-container">$(1+xr)$</span> is not invertible, it is contained in a maximal ideal which is <span class="math-container">$M... | It is the special case <span class="math-container">$\rm\ J = (x)\ $</span> in <span class="math-container">$\ (1) \iff (2)\ $</span> below.
<strong>Theorem</strong> <span class="math-container">$\ $</span> TFAE in ring <span class="math-container">$\rm\:R\:$</span> with units <span class="math-container">$\rm\:U,\:$<... | https://math.stackexchange.com |
79,936 | [
"https://softwareengineering.stackexchange.com/questions/79936",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/2114/"
] | Is it considered impolite to file a bug report against an abandoned open-source project, or an abandoned branch of a still-continuing project?
Is it perceived as making a request of the former author(s) of the project, which they're no longer willing to fulfil, or are bug reports merely seen as a description of the cu... | Impolite? No.
Why it should be? If it is abandoned it means nobody will look at hose bugs.
Useless? No.
If that project will start to live on, or it will be used in some project - people will see that bug reported and may take it into consideration. So you would help them, or in even better scenario - they will fix... | Why would it be impolite?
It my be unreasonable maybe, expecting that the author will deal with those bugs, errors, ... whatever, expecially if he explicitly said the project is abandoned, but impolite, no.
| https://softwareengineering.stackexchange.com |
526,279 | [
"https://physics.stackexchange.com/questions/526279",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/112034/"
] | I am going through an EM textbook and on the chapter on Gauss's law for electric fields, it discusses the field around an infinitely long charged cylinder with a linear charge density, say <span class="math-container">$\lambda$</span>. (EDIT1: <strong>uniform</strong> linear density)The author calculates the electric f... | The conceptually simplest mathematical proof I know uses a Coulomb's law integral over the charge distribution. This requires some knowledge of multi-dimensional integrals and matrices. It isn't the most condensed proof, but I think it is thorough and requires the least advanced math.
If you have some charge distribut... | It's not true in general that the electric field for this charge density has cylindrical symmetry. If you calculate a field for this charge distribution, and it satisfies Gauss's law, then you can always, for example, add a uniform field onto that. There are uniqueness and existence theorems for electrostatics, but the... | https://physics.stackexchange.com |
602,028 | [
"https://physics.stackexchange.com/questions/602028",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/281193/"
] | So, I had this question in mind for a few days now, suppose an object of mass <span class="math-container">$m$</span> is thrown up by a person.
Now, work done on the object would be stored in the form of potential energy, now it rises to a height <span class="math-container">$h$</span> and the person wants to stop the... | I think that this can be fairly simply answered, assuming that you're only considering a gravitational force. Although, I think you could still solve this problem with either quadratic or linear drag included (even though it would complicate things a little bit).
We know that the work done on an object is <span class="... | Your muscular energy used =mgh (this energy will used fully whether it goes to height h or h/2
When you throw want to stop it at h/2 some external force is required to stop it
<span class="math-container">$\int F_{ext}$</span>+<span class="math-container">$\int F_{non conservative}$</span> = <span class="math-container... | https://physics.stackexchange.com |
50,307 | [
"https://softwareengineering.stackexchange.com/questions/50307",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/15200/"
] | I was wondering if anyone had any resources or advice related to using architecture patterns like MVVM/MVC/MVP/etc on small applications and tools, as opposed to large, enterprisy ones.
EDIT:
Most of the information I see on application architecture is directed at large, enterprise applications. I'm just writing smal... | If your the only user and there are no deadlines or constraints why not rewrite it. It sounds like mainly an academic exercise anyway so you can't really lose.
| Leave it. Go find some users. If you can't find any, there's no need to rewrite it. If you do find users, they'll probably push your project in directions you never considered. These new directions will eventually break things and you'll be forced to rewrite. Change your tech then if it makes sense.
If this project is... | https://softwareengineering.stackexchange.com |
45,836 | [
"https://engineering.stackexchange.com/questions/45836",
"https://engineering.stackexchange.com",
"https://engineering.stackexchange.com/users/24283/"
] | Lets say we have a very large and deep circular footing for a tall tower such as an industrial chimney or a wind turbine, and for convenience we want to pour it not at once but in sections. Can this be done, provided that we have sufficient dowels between the pour sections? Or it must be a single pour?
| -Yes, it is possible and is routinely done.
A couple of concerns,
<ul>
<li>Massive concrete creates a huge amount of heat and thermal expansion, thus the elaborate systems of cooling the pour.
</li>
<li>Also the curing under different climates is not good so careful planning is needed.
</li>
<li>The cold joint should b... | Since the footing is "large and deep", <strong>both the vertical and horizontal construction or expansion joints can be utilized to partition the concrete pour.</strong>
Note, other than the capability/capacity of the concrete plant and crew to produce and handle the concrete placement, the amount of <strong>... | https://engineering.stackexchange.com |
17,169 | [
"https://physics.stackexchange.com/questions/17169",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/4023/"
] | How does a mobile phone vibrate without any external force? By Newton's law, any body can't move without any external force
| That's not true, Newtons's laws do not say that. What's important here is conservation of momentum. Inside the phone, there is an oscillating mass. While the mass inside has a momentum and thus a velocity in one direction, the (friction-free) phone has to have the same momentum in the opposite direction. It "vibrates".... | At least one mobile phone I've heard about uses an unbalanced spinning weight. As the weight moves in one direction, the phone moves in the other, in accordance with Newton's Third Law of Motion.
| https://physics.stackexchange.com |
465,177 | [
"https://electronics.stackexchange.com/questions/465177",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/72429/"
] | I have always had it in my head that gold plated contacts were preferred.
I noticed today that the resistivity is as follows:
Silver 1.5x10<sup>-8</sup>
Gold 2.4x10<sup>-8</sup>
Is there another property that makes gold preferable to silver for use in electrical contacts?
| Gold doesn't oxidize, which means that gold-to-gold contact has no extra resistance.
In other words, it isn't about the bulk resistance (the plating is very thin anyway), but about the contact resistance.
Silver is used in places where the resistance to current flow <em>along</em> a surface matters, such as the inter... | Gold doesn't oxidize, that is, its atoms don't lose electrons to an electron acceptor like oxygen or sulfur. There are trace amounts of hydrogen sulfide gas in the atmosphere, which is why silver tarnishes over time. The tarnish consists of a very thin layer of silver sulfide. Gold, however, is more inert than silver, ... | https://electronics.stackexchange.com |
10,276 | [
"https://stats.stackexchange.com/questions/10276",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/2310/"
] | I have a response variable measured at three time points per individual (week 0, 18, and 36). I am interested in differences in the change of the response over the 36 weeks within some categorical variable X.
I see two ways of modeling this.
<ol>
<li>One way ANOVA with response = <code>week_36_score - week_0_score</... | In general, I would go with a repeated measures design.
There is nothing technically wrong with the first option. However, you are essentially throwing away 1/3 of your data (and 1/2 of your non-baseline data!), which may result in a lost of power. Additionally, since you have a measurement in between baseline and 36... | There are difficulties in computing change. This doesn't work on ordinal repsonses, and for continuous responses makes a strong assumption of proper choice of transformations for the variables. I recommend adjusting for baseline and modeling the 2nd and 3rd measurements as longitudinal measurements.
Repeated measu... | https://stats.stackexchange.com |
289,499 | [
"https://softwareengineering.stackexchange.com/questions/289499",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/186048/"
] | I have seen other peoples code and each person has a different way of declaring variables. And I have been told by quite a few people that declaring variables in the Global Scope is wrong.
My question is why is it wrong and what is the correct way of declaring variables while writing any software, application or syste... | One of the problems of using global variables is that it can lead to conflicts when you use them with other modules that also uses the same variable names and are also declared global in those modules. Say you have a Javascript file call it main.js and in that file are codes where there are global variables A, B and C... | On problem with globally scoped variables is that it can make the understanding of who needs to use that variable or modify it more difficult. It also means that as code grows, there can be collisions in usage of the variable - not simply having the same name for what should be two variables, but separate usages of the... | https://softwareengineering.stackexchange.com |
34,690 | [
"https://electronics.stackexchange.com/questions/34690",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/10386/"
] | I was thinking to make a simple oscilloscope which can measure at least 2MHz signals, that would be enough, and it will be connected to a PC, or Android device.
First, I tought to use USB to connect the "oscilloscope" to the PC or Android USB Host capable device that would give me about 12Mbps transfer speed but I woul... | If you treat the PDA as simply a display, then you can change your way of thinking about what data actually needs to be sent. It only needs a single trace of data, the width of the display, up to 30 times per second. If we assume 8 bit samples, and a retina display width of 960 columns, then you only need to send 960... | There is no way to avoid this, you simply have to send less data.
Most scopes (including USB scopes running above the USB data rate) do not sample continuously. On triggering they fill a smallish buffer and send to display, then wait for another trigger, fill buffer, send to display and so on.
So you will have to ... | https://electronics.stackexchange.com |
327,730 | [
"https://softwareengineering.stackexchange.com/questions/327730",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/41448/"
] | We are developing a mobile app/apps which has two parties involved, creators and consumers. Creators first register themselves, get verified and then create the events. Consumers browse for desired events and if found interesting, register for the event.
What will be the best practice to achieve the above scenario. Tw... | Since there are no common features i suggest creating separate applications. That lets you update either app without confusing your users (e.g. updating an app without changing anything for the consumers).
Merging the two apps at a later point is probably easier than tearing one in half.
| Will creators never consume? Will consumers never create? If you can answer yes to both, then I would consider two applications. If not, then I would consider one application.
This seems similar to email. Reading is a consumption function, while write is a creator function. I haven't seen many useful applicatio... | https://softwareengineering.stackexchange.com |
888,174 | [
"https://math.stackexchange.com/questions/888174",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/90230/"
] | I tried solving the logarithmic inequality:
$$\log_2\frac{x}{2} + \frac{\log_2x^2}{\log_2\frac{2}{x} } \leq 1$$
several times but keeping getting wrong answers.
| Let $\log_2 x=A$, then $\log_2 x^2=2\log_2 x=2A$ and $\log_2\frac{2}{x}=\log_22- \log_2x=1-A$. So the given inequality becomes:
$$(A-1)+\frac{2A}{1-A} \leq 1.$$
Consequently we get
$$\frac{4A-A^2-1}{1-A} \leq 1.$$
Furthermore you get
$$\frac{5A-A^2-2}{1-A} \leq 0.$$
Hopefully you can solve from here.
| Put $u=\log_2\left(\dfrac x2 \right)=\log_2x-1$
Note that $\log_2(x^2)=2(u+1)$, and $\log_2\left(\dfrac 2x\right)=-u$.
Hence inequality becomes
$$ \begin{align}
u-\dfrac {2(u+1)}u \leq1\\
\dfrac{u^2-3u-2}u \leq0\\
\dfrac{(u-\alpha)(u-\beta)}u \leq 0\\
\end{align}$$
where $\alpha=\dfrac {3+\sqrt{17}}2,\ \beta=\dfrac... | https://math.stackexchange.com |
431,087 | [
"https://softwareengineering.stackexchange.com/questions/431087",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/400389/"
] | I've been tasked with re-designing a system that is, for lack of a better term, complete spaghetti. For various reasons I feel that the system is well-suited for microservices. At a high level I feel that every service should...
<ul>
<li>Function standalone</li>
<li>Not have direct dependencies on other services</li>... | <blockquote>
At a high level I feel that every service should [..] Not have direct dependencies on other services
</blockquote>
That is not necessarily a realistic expectation.
If we're talking <strong>functional</strong> dependency, microservices still depend on each other in the sense that service A may call service ... | <strong>Processing older data</strong>
Your question title is currently, "adding new service into existing microservice system". Looking at the body of your question, and particularly your line "The new service catching up to what has happened in the system while it didn't exist", the title of your ... | https://softwareengineering.stackexchange.com |
13,470 | [
"https://dba.stackexchange.com/questions/13470",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/6839/"
] | On my database structure in SQL Server, I have 3 types of products which requires different information about the order. So, I created one <code>Customers</code> table and three different orders tables: <code>OrdersForProductAs</code>, <code>OrdersForProductBs</code>, <code>OrdersForProductCs</code>. All orders table h... | I'd question why you have <code>OrdersForProductX</code> tables at all<br>
It's possible the FK problem you've asked about can be designed out...
If these tables have the same structure, then you simply need a <code>ProductType</code> column on some <code>OrderProduct</code> table. Then <code>Payment</code> just links... | Avoid nullable "foreign keys". They have multiple disadvantages.
The constraint on a referencing row is not always enforced when the foreign key contains a null. However, that default behaviour is not consistent between different DBMSs. Some DBMSs support configuration options to change the behaviour of nullable forei... | https://dba.stackexchange.com |
221,820 | [
"https://physics.stackexchange.com/questions/221820",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | from a classical perspective, what is it about angular momentum fundamentally that means it has to be conserved? Surely if I have a rod about a fixed axis and a moving particle hits the end it will cause the rod to spin and therefore create angular momentum? (The particle isn't spinning around a point after the collisi... | <blockquote>
Surely if I have a rod about a fixed axis and a moving particle hits the end it will cause the rod to spin and therefore create angular momentum?
</blockquote>
First off, there is no reason to expect that <em>any</em> of the conservation laws apply to the rod. A moving particle collides with the rod, an... | Angular momentum is conserved in any system which has no external torques exerted upon it (much as linear momentum is conserved in any system which has not external forces exerted upon it).
The example of a moving particle hitting something and changing that somethings angular momentum is not relevant, since the somet... | https://physics.stackexchange.com |
66,708 | [
"https://softwareengineering.stackexchange.com/questions/66708",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/226/"
] | Where I work we practice scrum-driven agile with 3-week iterations. Yes, it'd be nice if the iterations were shorter, but changing that isn't an option at the moment.
At the end of the iteration, I usually find that the last day goes very slowly. The actual work has already been completed and accepted. There are a cou... | I've been struggling with the same question a bit lately. We are starting on the next iteration, but I feel that this removes the satisfaction of an iteration well done.
I am thinking about the option of leaving it up to the developers, with the caveat "as long as the intent is to benefit the company."
Examples:
<ul... | Take the day off. You did the work you were supposed to get done so why are you still working?
If process change were possible, consider dropping iterations, release continually, and just keep pulling stories off the backlog. But don't you deserve a little down time?
| https://softwareengineering.stackexchange.com |
221,098 | [
"https://softwareengineering.stackexchange.com/questions/221098",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/103705/"
] | I'm developing a small system for internal automation. I use asp.net webforms and faced with a choice:
<ol>
<li>develop a system architecture in an object-oriented style (development becomes more difficult and time-consuming)
or
</li>
<li>just put controls on forms and write sql queries in control handlers (high speed ... | <h2>Flexibility vs. formalism</h2>
There is a continuum between projects which require no quality (e.g. prototypes) and the ones which need the highest quality possible (e.g. life-critical systems).
<img src="https://i.stack.imgur.com/0iGSe.png" alt="The diagram representing the described continuum">
On the left sid... | Ehy if you start coding putting things here and there then your project becomes a mess!
Follow method number 1, as you are doing now, it will pay later.
Consider that an automation system, for how small it can be, must guarantee a reliable and affordable service for a medium to long period of time.
If you don't use a... | https://softwareengineering.stackexchange.com |
2,768,994 | [
"https://math.stackexchange.com/questions/2768994",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/179809/"
] | Let $\,f: \mathbb{R} \rightarrow\mathbb{R}$ be some function st $f(0)=0$ and $f'(0) > 0$. Is it the case that $f$ must be increasing in some neightborhood of zero? If $f$ is differentiable in some neighborhood of $0$ then the answer is trivial with the MVT, however all we have is differentiability at a point. I don'... | Let
$$ f(x)=\begin{cases}x+2x^2\sin\frac1x&x\ne0\\0&x=0\end{cases}$$
This $f$ is continuous and has derivative
$$ f'(x)=\begin{cases}1+4x\sin\frac1x-2\cos\frac1x&x\ne0\\1&x=0\end{cases}$$
So $f$ is differentiable on all of $\Bbb R$, $f(0)=0$, $f'(0)=1$, and yet it is not increasing in any neighbourhood ... | The original statement is false, as the previous answer already showed.
However, a weaker statement holds: if <span class="math-container">$f$</span> is differentiable at a limit point <span class="math-container">$x_0$</span> with positive derivative <span class="math-container">$f'(x_0) > 0$</span>, then there exi... | https://math.stackexchange.com |
2,033,125 | [
"https://math.stackexchange.com/questions/2033125",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/382540/"
] | $$ e = \lim_{x \to ∞}(1+\frac{1}{x})^x $$
I think this is relevant from my textbook:
$$ \lim_{x \to ∞} \frac{e^x}{x^n} = ∞ $$
for all values of n.
How do I connect the two? Am I incorrect that they are related?
Thanks.
| The second limit cannot be used to determine $e$ as pointed out by Theophile.
Here is a proof for the first limit using only the properties of exponential functions and the definition of the derivative. I am not 100% sure of its validity and would appreciate any constructive criticism.
Define $e$ as the value of the... | Usually, we have
$$L=\lim_{n\to\infty}\left(1+\frac xn\right)^n$$
Taking the log of both sides and applying log rules and L'Hospital's rule,
$$\begin{align}\ln(L)&=\ln\left(\lim_{n\to\infty}\left(1+\frac xn\right)^n\right)\\&=\lim_{n\to\infty}\ln\left(1+\frac xn\right)^n&\text{bijective}\\&=\lim_{n\t... | https://math.stackexchange.com |
200,473 | [
"https://softwareengineering.stackexchange.com/questions/200473",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/13070/"
] | Let's say we're making a parser. One implementation could be:
<pre><code>public sealed class Parser1
{
public string Parse(string text)
{
...
}
}
</code></pre>
Or we could pass the text to the constructor instead:
<pre><code>public sealed class Parser2
{
public Parser2(string text)
{
... | Semantically speaking, in OOP you should only pass the constructor a set of parameters which are needed to build the class - similarly when you call a method, you should only pass it the parameters it needs to execute its business logic.
The parameters that you need to pass in the constructor are parameters which have... | Well, let's recall what it means to pass a variable as constructor parameter: You initialize an object in order to use its instance variables in methods of the object. The point is that you probably want to use it in more than one method since you want to have a <strong>high cohesion</strong> in your class.
Passing a ... | https://softwareengineering.stackexchange.com |
1,060,746 | [
"https://math.stackexchange.com/questions/1060746",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/187799/"
] | How can I prove
<blockquote>
$$1+2^n+3^n+4^n$$ is divisible by $10$ if $$n\neq 0,4,8,12,16.....$$
</blockquote>
| We consider it $(\mathrm{mod}\;2)$ and $(\mathrm{mod}\;5)$ separately.
Clearly $1$ and $3^n$ are odd, while $2^n$ and $4^n$ are even, so their sum is even.
Now by Fermat's Little Theorem, when $a$ is not divisible by $5$, $a^5 \equiv a \mod 5$, so $a^4 \equiv 1 \mod 5$. Thus we only need to check $n=1$, $2$, and $3... | $$3\equiv1\pmod2\implies 1+2^n+3^n+4^n\equiv0\pmod2$$
If $n$ is odd, $1+4^n=1^n-(-4)^n$ is divisible by $1-(-4)=5$
Similarly, $2^n+3^n\equiv0\pmod5,$
For $n=4k+2,2^{4k+2}\equiv4\pmod5,3^{4k+2}\equiv-1,4^{4k+2}\equiv1$
| https://math.stackexchange.com |
143,129 | [
"https://mathoverflow.net/questions/143129",
"https://mathoverflow.net",
"https://mathoverflow.net/users/4096/"
] | Can the fundamental group of a quasi-affine variety over $\mathbb{C}$ be a torsion group?
| The answer is <em>yes</em>, already for an affine variety.
The following example is taken from Dimca's book <em>Singularities and topology of hypersurfaces</em>, see page 102 and page 105. We work over $\mathbb{C}$.
Let $V \subset \mathbb{P}^n$ be a hypersurface and $U:=\mathbb{P}^n \setminus V$ its complement. Since... | A less interesting but personally checkable answer: consider $f : ({\mathbb C}^2 \setminus 0)/\{\pm 1\} \hookrightarrow {\mathbb C}^3$, $(x,y) \mapsto (x^2,xy,y^2)$. The image is the punctured quadric cone and obviously has fundamental group $\{\pm 1\}$.
| https://mathoverflow.net |
155,414 | [
"https://softwareengineering.stackexchange.com/questions/155414",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/53164/"
] | I have created a small application which has a three tier architecture and I have business object classes to represent entities such as <code>User</code>, <code>Orders</code>, <code>UserType</code> etc. In these classes I have methods that are executed when the Constuctor method of, for example, User is called. These m... | The theory:<br>
A class should be responsible for its data and know what to do with its data. Any methods that the class needs to enforce that responsibility should be within the class.
In Practice:<br>
So the class will have <code>User.Name</code> and it should also have <code>User.GetName(), User.GetFirstName(), Us... | If you want follow the OO principles, the answer to this question is yes. An object is responsible to manage its state and behaviour. This means that all the property and methods that describe the object should be implemented in the the base class.
This is a written rule, a theory.
Form the practical side, you can de... | https://softwareengineering.stackexchange.com |
6,420 | [
"https://security.stackexchange.com/questions/6420",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/4387/"
] | I'm a software developer but I'm marking my niche in secure development. It turns out that while using WebScarab, I discovered that a popular user group site doesn't appear to properly take care of web passwords: The login page is http, but the submit button links to an https link.
Using WebScarab I captured the pas... | @Hendrik is right to say that this is a security risk in that a non HTTPS login page may allow for an attacker to modify the submit link before the user clicks it, however to the point in your question around webscarab.
It (along with other proxies) does intercept HTTPS traffic (assuming that you've set it as a proxy ... | Yes, this is a security issue because an attacker may be able to change the HTML code. He can change the action attribute of the form to point to his own server. Or less obvious and better: Add some javascript code that mirrors the password to his own server without breaking the login to the real site.
Unfortunately b... | https://security.stackexchange.com |
95,399 | [
"https://electronics.stackexchange.com/questions/95399",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/30175/"
] | To handle an interrupt the processor jumps to an interrupt service routine (ISR). If this ISR generates the same interrupt then this can result in:
a) program error
b) hardware error
c) stack overflow
This is a question asked in a university entrance exam and I am a computer science student. Is it possible to hav... | The Popular Electronics article I remembered described a short distance communications system made by pumping the AUDIO from an AUDIO PA into the ground through two ground connections about 20 feet apart. To achieve an approximate match into the earth, they used an audio output transformer turned around backwards.
Th... | It's really not so easy to do that. You can't just pump energy into the ground; you have to have an antenna of some sort to transmit with. And for very low frequency, you need an antenna that is very, very long. Hundreds of meters to kilometers. And it's not going to be very efficient, either, so you're going to ne... | https://electronics.stackexchange.com |
124,940 | [
"https://mathoverflow.net/questions/124940",
"https://mathoverflow.net",
"https://mathoverflow.net/users/32274/"
] | Does anyone knows whether the set of the absolutely continous functions $F :[0,1]\to \mathbb{R}^d$ of the form $$F(t)= a + \int_0^tf(s) ds$$ where $f$ is an integrable function is a Borel set of the Banach space $C$ of the continuous funtions $$F : t\in [0,1] \to F(t)\in \mathbb{R}^d$$ with the norm of the uniform conv... | Let $\phi:C\to[0,\infty]$ be defined for $F\in C$ as the norm of $F$ in $W^{1,1}$ if $F$ is absolutely continuous, and $+\infty$ otherwise. Then $\phi$ is lower semi-continuous for the topology of uniform convergence and $W^{1,1}=\{\phi<\infty\}$ is Borel measurable.
| I think Bill Johnson's answer ``just use the definition" is correct, but that he did not write what he wanted to write. A function $f\in\mathcal C([0,1],\mathbb R^d)$ is absolutely continuous if and only if the following holds:
$$\forall p\in\mathbb N\; \exists q\in\mathbb N\; \forall x_1,\dots ,x_N,y_1,\dots ,y_N\in\m... | https://mathoverflow.net |
214,504 | [
"https://physics.stackexchange.com/questions/214504",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/96573/"
] | What would an operator look like that measures the following thing? We have a particle in one dimension. A lamp goes on if the particle is found in a certain interval on the real axis.
| Your operator should have eigenvalue 1 (lamp on) if the particle is found within some interval $x\in [0,L]$, and eigenvalue 0 (lamp off) otherwise. Such an operator would look like
$$ P_{[0,L]} = \int_0^L\mathrm{d}x \; \lvert x\rangle \langle x \rvert, $$
i.e. it is a projector onto the subspace spanned by position eig... | In general, the expectation value for any observable quantity is found by putting the quantum mechanical operator for that observable in the integral of the wavefunction over space: $$\langle Q\rangle= \int_{-\infty}^\infty \psi^*\hat{Q}\;\psi\; dV.$$
| https://physics.stackexchange.com |
302,052 | [
"https://physics.stackexchange.com/questions/302052",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/134870/"
] | Can you show me the maths behind this phenomena.
When two balls fall down in which one with bigger mass than the other and same shape, they both fall simultaneously.
| There is also a sort of "basic physics expectation" why this should happen, if you want to hear it.
Suppose an object of mass $2M$ fell faster than an object of mass $M$. Usually high-school students expect the first to fall, say, twice as fast, but it's not super-important what value it is.
Now imagine dropping two ... | F = GM$m_1$/$R^2$ with M the mass of the earth and R the radius of the earth. And the mass of the object is $m_1$
Let's say the mass is a few feet = h above the ground, so your distance to the center of the earth is R + h. Since h is so much smaller than R you can ignore it.
Then since F = $m_1a$, solve for a to gi... | https://physics.stackexchange.com |
53,850 | [
"https://electronics.stackexchange.com/questions/53850",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/2028/"
] | I'm designing a 12V battery-operated portable lighting controller, and frequently am asked about improving the run time. The simplest way is to add a second battery in parallel, but I often worry that users will get it wrong, hook up the batteries in series, and provide 24V instead.
What's the best/recommended way to ... | Something like this should work:
<img src="https://i.stack.imgur.com/ouPBj.png" alt="zener overvoltage protection">
Use 12V zener, choose a mosfet with low gate threshold preferably Vth < 3V, Vgs < 12V and capable of high instanteneous current.
If a voltage Vin gets above 12V, Vin - Vz will appear at the gate... | You're on the right track. The only solution is to isolate the load from the overvoltage. There are many ways to accomplish that, and a fuse (either single-use or resettable PTC) is one traditional approach. The zener/TVS makes sure that the circuit draws enough current in the presence of overvoltage to trip the fuse. ... | https://electronics.stackexchange.com |
61,638 | [
"https://stats.stackexchange.com/questions/61638",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/-1/"
] | In statistical hypothesis testing we decide on and <em>set</em> the acceptable probability of error or <strong>significance level</strong> α (alpha) to a value that fits our theory. Traditionally alpha is .1, .05, or .01.
When we <em>calculate</em> the power function g of the parameter we test for, we recieve the dist... | When doing a continuous test and all the assumptions hold then the 2 alphas are exactly the same thing. For example if I perform a t-test on a mean and set my significance level to alpha=0.05 (or anything else) and the null hypothesis is true (the only time I can make a type I error) and all the other assumptions hold... | When you are doing a statistical test, the significance level is set at the desired type I error level (alpha). So the concepts you are asking about are basically the same thing - both are fixed by design to the same value. The p-value is calculated from the data and is different from the alpha value, and may be why yo... | https://stats.stackexchange.com |
28,275 | [
"https://chemistry.stackexchange.com/questions/28275",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/11490/"
] | I'm specifically talking about the decomposition of hydrogen peroxide by bovine catalase. The number of catalase molecule obviously doesn't change, so there's the same number of catalase molecule within an undiluted and a diluted solution. Also, seeing as water is not an enzyme inhibitor, and doesn't change the pH or t... | <blockquote>
[…] there's the same number of catalase molecule within an undiluted and a diluted solution. Also, seeing as water is not an enzyme inhibitor, […]
</blockquote>
<strong>Q</strong>: Why is dating between a fixed number of guys and girls more difficult on a large square packed with nuns than... | If you diluted the catalase, <em>while keeping the peroxide concentration fixed</em> (by adding both water and peroxide to the solution), then you're right, the total reaction rate (measured in reactions catalyzed per second, within the whole solution) would not change.
However, by adding just water to the solution, y... | https://chemistry.stackexchange.com |
412,528 | [
"https://physics.stackexchange.com/questions/412528",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/166555/"
] | When I read about the superposition principle, it says that it works only on linear systems, my problem is that I cannot really understand the difference between a linear and a non-linear system. I cannot understand whether it means the order of the corresponding differential expression for that certain fields, or some... | <blockquote>
So if anybody can help me get the essence of linear systems and
differentiate between a non linear one
</blockquote>
Consider a simple <em>system</em> to be a black box with an input (stimulus) $x(t)$ and an output (response) $y(t)$.
Let $y_1(t)$ be the output given an input $x_1(t)$ and $y_2(t)$ be ... | This can sound somewhat circular, but the essence of it is this:
<blockquote>
a linear system is one that obeys the superposition system,
</blockquote>
by definition of the former. This means that the superposition principle holds in all linear systems, but it also means that this is a relatively trivial property,... | https://physics.stackexchange.com |
88,877 | [
"https://cs.stackexchange.com/questions/88877",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/63873/"
] | Code for finding $\phi$(n) is
<pre><code>int phi(int n)
{
int result = n; // Initialize result as n
// Consider all prime factors of n and subtract their
// multiples from result
for (int p=2; p*p<=n; ++p)
{
// Check if p is a prime factor.
... | The cost inner loop if $n$ is equal to $P_1^{a_1}P_2^{a_2}\cdots P_k^{a_k}$, should be run in $\log_{P_1}n + \log_{P_2}n + \cdots + \log_{P_k}n$ totaly which is $O(k\log(n))$.Notice that, these computation is computed over the outer loop and summation of all iterations of the outer loop.
To more scrutinizing, as the ... | Whenever you find a factor, n gets smaller. The amount of work needed to process one factor is trivial compared to the savings you get by dividing n by that factor.
| https://cs.stackexchange.com |
585,606 | [
"https://stats.stackexchange.com/questions/585606",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/26456/"
] | I would like to fit a one-way between-subject anova that <em>assumes unequal variances</em> between groups.
Reproducible example:
<pre class="lang-r prettyprint-override"><code>library(emmeans)
library(car)
set.seed(123)
n <- 50
DF <- data.frame(score = c(rnorm(n, sd = 10), rnorm(n, sd = 30), rnorm(n, sd = 40)),... | Found a way to do it via <code>lmer</code>:
<pre class="lang-r prettyprint-override"><code>library(lme4)
mdl <- lmer(score ~ treatment + (0 + treatment|subject), data = DF,
+ control = lmerControl(check.nobs.vs.nRE = "ignore",
check.nobs.vs.nlev = "... | You can do heterogeneous variance in a variety of ways in R. A simple way is through the <code>gls</code> package
<pre class="lang-r prettyprint-override"><code>library(nlme)
mod = gls(score~treatment, data=DF,
weights = varIdent(form = ~1|treatment),
method="ML")
emmeans(mod, ~treat... | https://stats.stackexchange.com |
314,018 | [
"https://softwareengineering.stackexchange.com/questions/314018",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/222152/"
] | I need some clear explanation and maybe an example of how frameworks like JavaFX, Tkinter etc. work.
Lets take Python's Tkinter. When I bind a button's action I just do
<pre><code>def callback():
print "clicked!"
b = Button(text="click me", command=callback)
</code></pre>
Somehow I give the callback function ... | In python, a <em>variable</em> can contain just about anything; that includes (but not limited to) a number, a string, a class object, or.. a function.
As you're probably already aware, the <em>usage of</em> (i.e. the things you can <em>do with</em>) a Python variable depends on whatever it happens to contain.
For e... | Like many dynamically-typed scripting languages, <strong>in Python functions are first-class values</strong>, which means they can be passed into and returned from functions just like any other ordinary value. So the direct answer to your question is "you just do it, there's nothing stopping you".
<pre><code>def squar... | https://softwareengineering.stackexchange.com |
48,804 | [
"https://electronics.stackexchange.com/questions/48804",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/2533/"
] | I'm responsible for maintaining a satellite that has an ADC that is failing in an unusual manner. Essentially what is happening is that it toggles back and forth between two values, if the raw voltage is in a certain range. I'm working on getting the raw counts, but the processed data looks something like this:
<img s... | Using the detailed information I am collecting, I am noticing the following trends:
<ol>
<li>There doesn't appear to be any complete gaps in the ADC range, except for areas where it appears there just wasn't any input signal.</li>
<li>There are a number of regions that look like the data below, where it seems that val... | Is there a reason to suspect the ADC over everything else in the system? Anything between the battery and the ground
station could be causing what you see. A good fault tree will consider other causes besides the ADC.
<ul>
<li>The analog front-end
<ul>
<li>radiation effects on op-amps and analog switches</li>
<li>op-... | https://electronics.stackexchange.com |
215,029 | [
"https://electronics.stackexchange.com/questions/215029",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/88607/"
] | I am a little confused on how to read the ratios of a transformer
Suppose there is a ratio of 1:6, is this read as the following?
Number of turns on Primary: Number of turns on Secondary?
so suppose a question asked that there is a voltage of 20 voltages rms and it enters a transformer of 1:6, is the Vout rms calcula... | I'll assume that multiplying by 8 was a typo, and that you meant 6, as your original ratio was 1:6.
The usual way to read it is the first number represents the primary, the second the secondary, so in your example you would have 120v output.
However, I know many people who describe all transformers in the style N:1, ... | most of the time 1:6 means the ratio of primary turns to secondary. then you will have 120v in secondary. wire guage those not affect the ratio.
| https://electronics.stackexchange.com |
92,099 | [
"https://mathoverflow.net/questions/92099",
"https://mathoverflow.net",
"https://mathoverflow.net/users/20343/"
] | I am currently writing a paper on non-standard models of Peano arithmetic and I am having trouble finding references or information that discuss the relative sizes of how many models of Peano arithmetic there are in the standard and the non-standard cases.
I see it quoted all over the place that, "It is familiar that... | Here is another way to do it.
By the Gödel-Rosser theorem, there are continuum many distinct consistent completions of PA. One can see this by building a tree of finite extensions of PA, using the Gödel-Rosser theorem at each node to branch with the Rosser sentence or its negation relative to that theory (a... | For any set $S$ of (standard) prime numbers, there is, by a compactness argument, a non-standard countable model $M(S)$ of PA containing an element divisible by exactly the primes in $S$. (Actually there are many such models but I need just one.) The same model $M$ might serve as $M(S)$ for several differnt $S$´s, bu... | https://mathoverflow.net |
2,516,752 | [
"https://math.stackexchange.com/questions/2516752",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/557708/"
] | Let $f(r,\theta)=(r\cos\theta ,r\sin\theta)$ for $(r,\theta)$ $\in \mathbb R^2$ with $r\ne0$.
then which are true statements?
a) f is one -one on {($r$,$\theta$) ∈ $R^{2}$: $r\ne0$ }
b)for any ($r$,$\theta$) $\in$ $\mathbb R^2$ with $r\ne0$ ,f is one -one on a neighbourhood of ($r$,$\theta$)
my attempts :i know... | <strong>Hint</strong>
a) No. $f(1,0)=f(1,2\pi)$.
b) Yes. Fix $\theta $. We can suppose WLOG that in $]0,\infty [\times ]\theta-\pi ,\theta +\pi[$ it's one to one. I let you prove that.
| What happen for the points $(\frac{-1}{\sqrt2}$, $\frac{3\pi}{4})$ and $(\frac{1}{\sqrt2}$, $\frac{-\pi}{4})$ ?
In the order pair for $\mathbb{R}$$^2$ these points are different but they take the function to the same range value which is $(\frac{1}{2}$, $\frac{-1}{2}$$)$.
So in general it may not be one to one.
| https://math.stackexchange.com |
471,535 | [
"https://physics.stackexchange.com/questions/471535",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/223029/"
] | I wanted to find a creative solution to the problem:
<strong>Find the electric potential energy of a uniformly charged sphere of radius <span class="math-container">$R$</span> possessing a charge <span class="math-container">$Q$</span>.</strong>
My attempt at a solution:
Consider a gaussian surface, basically a sph... | After reading the comment you have made below, I came to realize that the real deal here is that the electric field is not varying as <span class="math-container">$x$</span> outside the sphere.
The problem here is not the integral (I apologize for that as I did not cross-check). In fact, it seems you are not very cle... | This can be proven.
Potential energy = <span class="math-container">$\frac{1}{2}\int VdQ$</span>
<span class="math-container">$dQ=\rho d\tau$</span> where <span class="math-container">$d\tau$</span> is the volume element.
So <span class="math-container">$PE=\frac{1}{2}\int V\rho d\tau=\frac{1}{2}\int \epsilon_0V(... | https://physics.stackexchange.com |
59,255 | [
"https://electronics.stackexchange.com/questions/59255",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/19478/"
] | I have a 12VDC 500mA power supply and I want to power two (2) separate items, by using a "Y" adaptor. The first item is supposed to use this exact power supply, but the second item tells me to use a 12VDC 250mA power supply. They are both a couple different projects with LEDs. I do not want to use two (2) separate powe... | The power supply is simply not powerful enough.
If you have two devices, of the same voltage rating (12V), you add the currents together to find out how much current your PSU needs to supply:
Device 1: 12V, 500mA<br>
Device 2: 12V, 250mA
Total current needed: 750 mA<br>
Total current your supply can handle: 500 mA
... | You have only one 6 watt rated power supply, but you want to source 9 watts. Best case scenario: it might work for a few seconds but then slowly the voltage will begin to drop and your power supply gets very hot. Absolute worst case scenario, after a while the PSU gets so hot it catches on fire due to a short OR overl... | https://electronics.stackexchange.com |
13,240 | [
"https://mathoverflow.net/questions/13240",
"https://mathoverflow.net",
"https://mathoverflow.net/users/434/"
] | Something that seems to be pretty standard in every introductory treatment is that the infinite places correspond to embeddings into $\mathbb{C}$. Do the finite places correspond to embeddings as well? I can envision two possibilities. My first guess is that the primes sitting above $p \in \mathbb{Q}$ correspond to ... | The Archimedean places of a number field K do not quite correspond to the embeddings of K into $\mathbb{C}$: there are exactly $d = [K:\mathbb{Q}]$ of the latter, whereas there are
$r_1 + r_2$ Archimedean places, where:
if $K = \mathbb{Q}[t]/(P(t))$, then $r_1$ is the number of real roots of $P$ and $r_2$ is the numb... | I'm not sure why Pete stopped short of coming back to the original poster's description in terms of embeddings. The point is that the infinite places of a number field $K$ correspond to embeddings of $K$ into $\mathbb{C}$ <i>up to equivalence</i>, where two embeddings are considered equivalent if one can be obtained f... | https://mathoverflow.net |
4,287,210 | [
"https://math.stackexchange.com/questions/4287210",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/478687/"
] | Let <span class="math-container">$Z$</span> be a centered normal variable of variance <span class="math-container">$\sigma^2$</span>, I am trying to prove that,
<span class="math-container">$$\sup_{t>0} \left( \mathbb{P}(Z \geq t) \exp\left( \frac{t^2}{2 \sigma^2} \right) \right) = \frac{1}{2} $$</span>
I have prove... | Let <span class="math-container">$Q(x)$</span> denote the <em>complementary</em> standard normal CDF given by
<span class="math-container">$$Q(x) = \int_x^\infty \frac{1}{\sqrt{2\pi}}\exp\left(-\frac{t^2}{2}\right) \, \mathrm dt.$$</span> Suppose that <span class="math-container">$t > x > 0$</span>. Since <span c... | Substitute <span class="math-container">$z = t/\sigma$</span> to simplify notation. You need to show that the function <span class="math-container">$$f(z) := \dfrac{1}{\sqrt{2\pi}}e^{z^2/2}\int_{z}^{\infty}e^{-u^2/2}\,du$$</span> is decreasing over <span class="math-container">$z > 0$</span> so that you can conclude... | https://math.stackexchange.com |
13,068 | [
"https://mechanics.stackexchange.com/questions/13068",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/3988/"
] | I only drive during the weekends, so most of the time my car is always in the garage. I have not been able to buy myself an air compressor, so what I do is I always have my tires check at my local gas station, which is about a kilometer away from my house. Now I have experienced problems with my tires, even if they are... | First of all, the short amount of driving you do prior to getting them refilled is not going to cause the tire itself any problems. The biggest problem you'll see with tires which are run low is the amount of heat build-up in the rubber. Not only is the low pressure not really that low, the distance you drive is not en... | This topic is pretty covered, but instead of using normal air, ask your tyre dealer to put nitrogen in your tyres. The compounds are a lot thickers and don't leak out as much as air does. My weekly air pressure checks are now every 3 months which it will only go down by 3 PSI.
| https://mechanics.stackexchange.com |
335,437 | [
"https://math.stackexchange.com/questions/335437",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/60334/"
] | For any positive integer $n$ let:
$$S_n = \{1,2,\ldots,n\}$$
(a) for any integer $n \ge 2$, find the number of 2-element subsets of $S_n$ which contain 2.
(b) for any integer $n \ge 2$, find the number of subsets $A$ of $S_n$ with the property that $N(A) \in A$ where $N(A)$ is the cardinality of the set $A$. Answer ... | HINTS:
(a) Picking a $2$-element subset of $S_n$ that contains $2$ is the same as picking a single element from $S_n\setminus\{2\}$.
(b) Let $f(n)$ be the number of subsets of $S_n$ with the property in question. There is $1$ $1$-element subset containing $1$. The answer to (a) is the number of $2$-element subsets co... | Here's another way, choose $2$ in the beginning. Now you have to choose one more element from the set $(1,3,4,5,6..n)$.
That is you can choose one element from the set in $n-1 \choose 1$=$n-1$
Therefore, there are $n-1$ subsets which has two elements with $2$ has one of its elements in total.
| https://math.stackexchange.com |
25,671 | [
"https://stats.stackexchange.com/questions/25671",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/6479/"
] | I'm totally not a pro in statistics so i hope the question is not too simple!
I have two groups of patients. One group are smokers, the second are non-smokers.
I want to compare the level of some hormones in the two groups to see if they are influenced by smoking. On many articles I found researchers using Mann-Whit... | First, a thought: Stop worrying about significance. For example, for the Spearman correlation, you have a (fairly) similar effect estimate to the Pearson test. Same direction, roughly the same magnitude. On a subjective level, you'd say the same thing. The only difference is the p-value. Would your answer, the "takeawa... | I'd suggest that you have a look at a graph of the distribution of scores in each of your groups- either a histogram or a density plot, where your score (in this case the hormone level) is on the x-axis and the count or proportion of people with that score is on the y-axis. I'm not sure what software you're using, but ... | https://stats.stackexchange.com |
203,509 | [
"https://dba.stackexchange.com/questions/203509",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/104360/"
] | I have the following table definition:
<pre><code>CREATE TABLE `async_task` (
`idasync_task` bigint(20) unsigned NOT NULL AUTO_INCREMENT,
`idasync_type` int(10) unsigned NOT NULL,
`priority` tinyint(3) NOT NULL,
`status` enum('todo','doing','failed') NOT NULL DEFAULT 'todo',
`iduser` int(11) NOT NULL,
`dat... | Both the referencing and referenced columns must be of the same type (and same in this case includes the <code>unsigned</code> attribute).
You didn't define <code>notification.async_task_id</code> as unsigned, so it was created with the (default) <code>signed</code>. Fix that and the foreign key will raise no errors. ... | also the character set of the two tables may be different.
Do a "SHOW CREATE TABLE table1" and "SHOW CREATE TABLE table2" and pay attention to the ending like DEFAULT CHARSET=utf8 or DEFAULT CHARSET=utf8mb4, those are not the same and can't have FKs pointing between them.
| https://dba.stackexchange.com |
85,183 | [
"https://mechanics.stackexchange.com/questions/85183",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/65145/"
] | I have a 2004 Subaru Impreza WRX with 212,000 miles. I have some paperwork on the past history of the car, but I don't see anything that refers to the transmission oil being changed (The transmission is automatic). I have had the head gasket replaced recently and the engine is in great shape. I am a little concerned, h... | If this were my vehicle, I would change the transmission fluid and filter. There is a baseless school of thought, more like an "old wives tale" that you will just cause damage by changing the fluid in an automatic transmission. But that is just a myth!
ATF is oil and oils break down over time, particles get... | This has the risk (albeit a small one) of making your transmission quit on you. Changing the fluids won't damage anything per se, but since the trans has 200k+ miles on it with no documentation on it ever having been serviced, the internals may be worn out and the only thing keeping it running may be the filth.
Kind of... | https://mechanics.stackexchange.com |
367,191 | [
"https://softwareengineering.stackexchange.com/questions/367191",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/197718/"
] | Reading "Code Complete 2" in a <strong>Quality of Requirements</strong> paragraph I found this:
<blockquote>
Are acceptable trade-offs between competing attributes specified — for
example, between robustness and correctness?
</blockquote>
<em>(this above is a point of a large checkbox list in order to check the q... | There are many situations in which these two might be in conflict. For instance, robustness can involve resilience under heavy load. If an approximate (i.e., incorrect) response to a request can be computed much faster than an exact (correct) response, it's important to know whether the system should deliver an approxi... | These two are just examples as you said. In fact, all non-functional requirments of that sort can potentially conflict with each other. In the book "Building Evolutionary Architectures" there is a table of roughly a hundred of these "-ilities" (as they are also often called).
It is sort of an exercise for software arc... | https://softwareengineering.stackexchange.com |
1,683,032 | [
"https://math.stackexchange.com/questions/1683032",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/283716/"
] | Here $V$ is a vector space and $\alpha =\{v_1,...,v_n\}$ is a basis for $V$. Let $T:V\rightarrow \Bbb{R}^n$ defined by $T(x)=[x]_{\alpha}$ for every $x\in V$. How to show $T$ is linear transformation and bijective?
To show it's a linear transformation, we have to show that $T(ax+y)=aT(x)+T(y)$, but how are we gonna sh... | To show that, e.g., $T(ax) = aTx$ for $x\in V$ and $a\in\mathbb R$, let $x\in V$, $a\in\mathbb R$. Then $x = c_1v_1 + \ldots + c_nv_n$ with some $c_1,\ldots,c_n\in\mathbb R$. You have $[x]_\alpha = (c_1,\ldots,c_n)^T$. Since $ax = ac_1v_1 + \ldots + ac_nv_n$, you also have that $[ax]_\alpha = (ac_1,\ldots,ac_n)^T$. Hen... | T is injective since $T(x_1)=T(x_2) \implies [x_1]_\alpha = [x_2]_\alpha$ which suggests that if $x_1=\sum_{i=0}^na_iv_i$ and $x_2=\sum_{i=1}^nb_iv_i$ then by the given condition $a_i=b_i$ for each $i$ in one through $n$ which implies that $x_1 = x_2$. Therefore $T$ is injective.
Also observe that $V = L(\alpha)$ i.e.... | https://math.stackexchange.com |
132,229 | [
"https://electronics.stackexchange.com/questions/132229",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/37879/"
] | Was wondering about the possibility of creating a magnetic field in milliseconds or less? I know it's possible based on certain labs achieving 60-100 Tesla and more. But what about creating a 2 - 5 Tesla magnetic field in milliseconds? How much power will be required? How will the electromagnet be designed?
Typically... | The magnetic field depends directly on the amount of current through the coil. To overcome the reactance (due to inductance) of the coil, use a high voltage. Follow that with a current regulator set to the value that gives you the 2-5T field. The higher the voltage used, the faster the current will rise to the desir... | you'd want to lower the inductance of the coil (di/dt) by connecting each loop of wire in parallel, instead of using a single coil of 20 loops you'd use 10 coils of 2 loops in paralel
| https://electronics.stackexchange.com |
78,810 | [
"https://electronics.stackexchange.com/questions/78810",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/15955/"
] | I have a pcb with a SPI bus with several sensors that have to be connected to this bus. Since 90 degree traces are not recommended in a proper PCB design I ask myself how to connect so many sensors without using sharp turns and perpendicular traces?
I am thinking about making triangles to smooth the connections, but I... | Quick answer: 90 deg bends are not an issue for most things. I don't do them purely from as aesthetic point of view. It only becomes an issue somewhere higher than about 500 MHz, but even then it's questionable.
There are three reasons to not do 90 deg bends: It causes an impedance mismatch, and thus messes up s... | As you guessed, at 20 MHz you will have no problem designing with 90 degree bends. You probably don't even need to worry about setting up your trace geometry to obtain a controlled-impedance microstrip or stripline.
If you were designing at 50 MHz or higher, you would probably want to design with a trace geometry that... | https://electronics.stackexchange.com |
449,671 | [
"https://math.stackexchange.com/questions/449671",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/62839/"
] | I'm working on the following exercise (not homework) from Ahlfors' text:
" If $f(z)$ is analytic in $|z| \leq 1$ and satisfies $|f| = 1$ on $|z| = 1$, show
that $f(z)$ is rational."
I already know about the reflection principle for the case of a half plane, so I tried using the "Cayley transform" $$T (\zeta)=\frac{\z... | In the given situation, we can proceed directly. The reflection in the unit circle is given by
$$\rho(z) = \overline{z}^{-1},$$
so by setting
$$g(z) = \frac{1}{\overline{f(\overline{z}^{-1})}},$$
we obtain a function $g$ that is meromorphic in the outside of the unit disk. Since $f$ can have only finitely many zero... | First note that the hypothesis implies that $f$ has only a finite number of zeros in the unit disk $\mathbb{D}$, say $\alpha_1, \dots, \alpha_n$. Consider now the function
$$B(z):=\prod_{j=1}^n \frac{z-\alpha_j}{1-\overline{\alpha_j}z}.$$
This is a <em>finite Blaschke product</em> and $|B(z)| =1$ for all $z \in \partia... | https://math.stackexchange.com |
150,847 | [
"https://physics.stackexchange.com/questions/150847",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/62834/"
] | Graphene is always in the news now a days and its key features are that it is; very strong, conductive and <strong>transparent</strong>. It is so transparent that each layer of graphene will only absorb 2% of Light passing through it.
But what is it about the <strong>structure of Graphene</strong> which makes it <em>(... | Graphene is only transparent because it is very thin (one atom thick). If it absorbs 2% per layer then just a few hundred layers would absorb almost all light and that would still be a very thin sheet of graphite.
The question should be why does graphene absorb so much light compared to diamond which really is transp... | I assume the biggest factor is the thickness. Graphene is a layer of carbon one atom thick. Light is absorbed/reflected by the top layers of a material and if you make any material into a layer one atom thick you'll find it increases transparency a lot.
The thing that is special about graphene is that it forms bonds ... | https://physics.stackexchange.com |
174,207 | [
"https://dba.stackexchange.com/questions/174207",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/98541/"
] | I wanted to know that, can I restore backup of SQL Server 2016 Standard edition database into SQL Server 2016 Express edition database.
Or vice-versa
| Sometimes:
<ul>
<li>When restoring into Express Edition, the database size can't be larger than the size supported by Express (which varies by version)</li>
<li>When restoring into Express or Standard Edition from Enterprise or Developer Edition, if your database uses Enterprise-level features, the recovery portion of... | Yes you can. Right click on your databases in SSMS (Task -> Back up) and create a back-up of your database, move it to the other host and restore it by right clicking on the server name in SSMS and chosing Restore.
Note that some functionality does not work in an Express edition (e.g. SSIS and SQL Agent).
| https://dba.stackexchange.com |
22,989 | [
"https://stats.stackexchange.com/questions/22989",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/8013/"
] | We are interested in fitting a multiple logistic regression model using data obtained from a national survey of children with special health care needs. The data has an accompanying weight variable intended to standardize children to the national population in which we intend to make inference. This weight variable doe... | Most stats software that is not built specifically for survey weights-to-population interprets weights as either a frequency variable or as a correction for heteroscedasticity and fits likelihood functions accordingly. Estimates of parameters will be correct but standard errors will be wildly wrong (usually way too sm... | In order to compute standard error correctly when dealing with complex sampling design (like e.g. stratified, cluster or stratified cluster or even multistage stratified cluster sampling) one needs to take into account two things:<br>
1. Probabilities of inclusion for every observation.<br>
2. Sampling design, definin... | https://stats.stackexchange.com |
518,140 | [
"https://electronics.stackexchange.com/questions/518140",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/208358/"
] | I am trying to design electrical wiring for a small 1-bedroom house which will be only powered from solar panels. The minimum appliances in a house would be:
Appliances available in 12V DC:
<ol>
<li>LED lights</li>
<li>Ceiling fans</li>
<li>Washing machine</li>
<li>Refrigerator</li>
<li>Air conditioner</li>
<li>Mobile ... | Your appliances fall into three categories:
<ol>
<li>Washing machine, air conditioning
</li>
<li>Refrigerator
</li>
<li>Everything else.
</li>
</ol>
Category 1 drives your requirements, especially A/C for a house.
Basically, you'll need both a fairly large inverter and a large battery bank to provide AC for these units... | A main driver will be your most power-hungry appliances. Washing machines will likely require around 2 to 3kW. it won't be practical to run one from an extra low voltage supply, through a "small" inverter. You would be looking at substantial cables (perhaps 25mm² or more), and a large inverter with a surge... | https://electronics.stackexchange.com |
233,264 | [
"https://dba.stackexchange.com/questions/233264",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/175681/"
] | We have the following architecture of our system (PostgreSQL 9.6 is used on all servers):<br>
1. there is a bunch of little servers ("sensors") storing data in some table<br>
2. there is a big server ("management console") that collects data updates from all those servers and stores them in the table with the same name... | OK, folks, thanks for your answers, but I've finally found a solution and tested it.
So, you will need to use pglogical (didn't test other replication tools, they might work as well) and create subscriptions on both sides - one subscription on a sensor and one subscription for each sensor on the console. This will sol... | Our company works with a technology called <strong>symmetric-ds</strong> to replicate our tables, from server to client, and from client to server. Take a look at the site.
| https://dba.stackexchange.com |
618,248 | [
"https://physics.stackexchange.com/questions/618248",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/290703/"
] | When I was studying motion, my teacher asked us to derive the equations of motion. I too ended up deriving the fourth equation of motion, but my teacher said this is not an equation. Is this derivation correct?
<span class="math-container">\begin{align}
v^2-u^2 &= 2ax \\
(v+u)(v-u) &= 2 \left(\frac{v-u}{t}\righ... | The problem of perception as to "What is a new Equation of Motion?" seems to originate with the dogmatic teaching of the Three Equations Of Motion as a Set of Results to be Learned.
They are in fact three results derived from the distillation of Newton's Laws:
<span class="math-container">$$\mathbf f = \dfrac... | There's nothing wrong with your calculation. But plug in <span class="math-container">$v=u+at$</span> and you find:
<span class="math-container">\begin{equation}
x=(u+at)t-\frac{at^2}{2} = ut + \frac{at^2}{2}
\end{equation}</span>
which is already one of your three equations of motion. So your teacher is probably just ... | https://physics.stackexchange.com |
361,860 | [
"https://softwareengineering.stackexchange.com/questions/361860",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/290214/"
] | I've been in an argument at work about writing readable code. It was mainly about variable and method names and the idea that comments are worthless if the code is readable enough. I would not like to emphasize only on no specific coding language.
1.) <strong>Descriptive vs minimalistic variable and method names</stro... | After reading the related question mentioned in the comments, I guess I understood your problem.
You could insert a new item at the end of the list, assigning it to some "sortOrder" that represents the last position.
After that, you implement some feature for changing the order of the items, by enabling the user to m... | <strong>It's almost always a bad idea to store a sort order persistently.</strong>
In order to be useful in a user interaction, there must be an obvious reason for things being in some specific order. That reason is almost certainly going to be easily calculable, and it will be easier to retrieve things as they are an... | https://softwareengineering.stackexchange.com |
254,301 | [
"https://softwareengineering.stackexchange.com/questions/254301",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/69801/"
] | This problem seemed like something which should be solvable with but a few lines of code.
Unfortunately, once I actually started to write the thing, I've realized it's not as simple as it sounds.
What I need is a set of X random numbers, each of which is between A and B and they all add up to X. The exact variables f... | As said before, this question actually doesn't have an answer: The restrictions imposed on the numbers make the randomness questionable at best.
However, you could come up with a procedure that returns a list of numbers like that:
Let's say we have picked the first two numbers randomly as -0.8 and -0.7. Now the requi... | Simple, as long as you know how many.
<ol>
<li>You need N numbers called V1 to Vn. The required sum is S. </li>
<li>Generate N random numbers (in any convenient range). They are R1 to Rn.</li>
<li>Calculate their sum as SR.</li>
<li>Scale each number so Vn = Rn * S / SR.</li>
</ol>
You may produce a tiny rounding err... | https://softwareengineering.stackexchange.com |
223,058 | [
"https://softwareengineering.stackexchange.com/questions/223058",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/113066/"
] | Consider a database table of Items that have a status flag represented by an integer. A few of the status might be:
<pre>
0 - Past Storage;
1 - Current Inventory;
5 - Scrap;
6 - Rework;
15 - Processing;
</pre>
Now, I would like to avoid passing and querying for 'magic numbers' in my code, and in the past I have used ... | Where I work this is a common situation. What we do here is use enums AND a separate table with the status flag as the primary key. In our experience, things have been a lot easier when the primary key was not an identity field. The good thing about doing it this way is that the c# compiler has a list of valid values (... | Usually integers can be represented by enums in code, as that will make it more readable for code blocks that use the integer.
Example:
<pre><code> public enum StatusFlag
{
PastStorage = 0,
CurrentInventory = 1,
Scrap = 5,
Rework = 6,
Proces... | https://softwareengineering.stackexchange.com |
546,266 | [
"https://physics.stackexchange.com/questions/546266",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/251156/"
] | I was reading the book of Wald on General relativity. And in the page number (33) he derives the equation for the action of <span class="math-container">$\nabla_{a}$</span> over a tensor of rank <span class="math-container">$(k,l)$</span>.
This is the equation (3.1.14):
<span class="math-container">$$\nabla_{a} T^... | <span class="math-container">$\nabla_a$</span> is a covariant derivative. In the context instead of <span class="math-container">$\partial_a$</span> is used <span class="math-container">$\tilde\nabla_a$</span>. <span class="math-container">$C$</span> coefficients are the connections, and another name for them is Christ... | The Christoffel symbols are a certain set of symbols that are defined by certain derivatives of the metric invariant of your choice of connection. The <span class="math-container">$C$</span> symbols which I assume here is the connection will equal the Christoffel symbols if you require the covariant derivative to be me... | https://physics.stackexchange.com |
12,957 | [
"https://mathoverflow.net/questions/12957",
"https://mathoverflow.net",
"https://mathoverflow.net/users/2024/"
] | <h3>Question</h3>
Given an abelian variety $V$ and an integer $n$, is there a natural abelian category with a natural object $X$ and natural coefficients $F$ so that $V\simeq H^n (X,F)$?
<h3>Motivation</h3>
Studying abelian varieties is awesome. Studying objects in long exact sequences is awesome. How do (somewhat f... | Let $\mathcal{A}/S$ be an Abelian scheme. Then the dual Abelian scheme is given by $R^1\pi_*\mathcal{A}$, if I remember correctly. Also, $\mathcal{A}^\vee(V) = \mathrm{Ext}^1_V(\mathcal{A},\mathbf{G}_m)$.
| You probably want the isomorphism above to respect some additional structures; otherwise if we view $V(\bar k)$ (assuming $V$ is defined over a field $k$) as just an abelian group, then take any finitely generated group $G$ (say the trivial group) and endow it with the trivial action on $V(\bar k)$, we will have $H^0(G... | https://mathoverflow.net |
702,470 | [
"https://physics.stackexchange.com/questions/702470",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/186828/"
] | I want to calculate the energy consumption in watts of the human body from calories consumed. My number is different than the expected value. Does anyone know where I'm going wrong?
<span class="math-container">$$E_{\rm day} = \rm 1900\,{cal} = 4.1\,\frac J{cal} \cdot 1900\,{cal} = 7790\,J$$</span>
<span class="math-... | (1) The value in calories that you've taken is very likely in food calories (<span class="math-container">$\text{Cal}$</span>), because <span class="math-container">$1\,900\,\text{cal}$</span> a day is too little for an average human. The conversion is:
<span class="math-container">$$1\,\text{food calorie (Cal)} = 1\,0... | <blockquote>
energy consumption in watts
</blockquote>
watt is unit of power, which is joule/second, i.e. energy/time.
1 kcal is 4184 J. 1900 kcal is 7.949.600 J.
1 day has 24 hours or 1440 minutes or 86400 seconds.
7.949.600 J/day equals 92 J/second or 92 W. This number is close to basal human metabolism rate.
If you ... | https://physics.stackexchange.com |
63,939 | [
"https://mathoverflow.net/questions/63939",
"https://mathoverflow.net",
"https://mathoverflow.net/users/7614/"
] | Where can i find material about the definition of the exponential morphism from the Lie algebra of an algebraic affine group to the group?
| In the classical theory of Lie groups and Lie algebras, the exponential map defined in terms of the usual power series is a standard tool for passing from the Lie algebra to the group. This makes sense for matrix groups over the real and complex fields because the series converges when evaluated at a square matrix, et... | Could be that Takeuchi's approach from "A hyperalgebraic proof of the isomorphism and isogeny theorems for reductive groups" is what you want. Steinberg in his lecture notes uses a slightly modified version of it (he doesn't mention any Hopf-theoretic stuff, though).
| https://mathoverflow.net |
44,926 | [
"https://mechanics.stackexchange.com/questions/44926",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/29010/"
] | My classic 350CC is a months old and 1st service is done. Post 1st service in the recent days i have expereinced an issue that when bike is in moving condition it automatically stops. The fuel tank has close to 6 ltrs of fuel and set the fuel nob to ON. I immediately changed the fuel nob to Reserve and the bike started... | News flash, Honda doesn't make anti-freeze. :D
You can use any non-silicate coolant meant for aluminium engines. Go to your local auto parts store, they'll show you which ones they have.
The most important thing is to thoroughly flush your cooling system first to make sure there is no trace of the previous coolant. I... | There are other coolant brands such as Prestone, Aisin... made specific for Japanese and European cars include Honda. Most of these are not sold on department stores but from auto parts store or online order.
| https://mechanics.stackexchange.com |
92,124 | [
"https://softwareengineering.stackexchange.com/questions/92124",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/54/"
] | I often hear people say they "sanitize input," which would mean make it clean. I understand this to mean "clean of potentially damaging contents," where the function that does the sanitizing would do something like character escaping.
But then I hear things like "sane input," which to me, means the input isn't a strin... | Sane input means input that is acceptable for further processing. It doesn't have to be dangerous - just wrong. Say,
<ul>
<li>fractional amount of items that are sold only in whole units. </li>
<li>A person's name containing newline characters.</li>
<li>A PO Box address for paid-upon-receiving parcel.</li>
<li>A valu... | Something everyone seems to overlook: "to sanitize" means "to make sanitary", i.e. to clean up, not "to make sane".
Thus, "sanitizing input" means cleaning up input by normalizing it or removing bad or unnecessary parts, but with the basic asssumption that the input is generally sane but possibly flawed in some aspect... | https://softwareengineering.stackexchange.com |
106,576 | [
"https://softwareengineering.stackexchange.com/questions/106576",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/35719/"
] | When asking an interview candidate to write a program on the whiteboard, do you expect the candidate to write code that is syntactically correct?
I had two candidates, one of which wrote a syntactically correct program but the logic was not up to the mark, and the other had the logic better written but the syntax was ... | I would favor the person who was able to reason through the problem, come up with a good solution, and then explain their solution to me. Even if their logic wasn't 100%, if they were on the right track and were reasoning through the problem, asking the right questions, and going down the right path, that would be my w... | I would favour the second candidate. Logic can be hard (<em>very</em> hard, sometimes) to get <em>exactly</em> right. Syntax can be <em>very</em> easy to get right when the IDE and compiler and other assorted tools help out.
The first candidate may never trigger a compiler error, but if his code often fails in all sor... | https://softwareengineering.stackexchange.com |
1,243,264 | [
"https://math.stackexchange.com/questions/1243264",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/80473/"
] | I need to compute $$\int \frac{(x-1)\sqrt{x^4+2x^3-x^2+2x+1}}{x^2(x+1)}\ dx.$$ I tried it on wolfram but it timed out, maybe because I am on a mobile device. Any hint is appreciated.
| Indeed they are both equal.
Let $P$ be the original price prior to any discounting or tax. Let $F$ be the final price after tax.
Now let us consider the two scenarios A and B.
<strong>Scenario A</strong>
After applying 6% tax, the price becomes, $1.06P$
Thus after the discount,
$F = 0.8\times1.06P$
<strong>Scen... | They are equal.
If the original price of the item is $P$, then
$$A=0.80\times(1.06\times P)$$
while $$B=1.06\times(0.80\times P)$$
Because multiplication of real numbers is associative and commutative, these are both equal to $$0.848\times P$$ and so are the same.
<strong>Comment:</strong> You may get the wrong answ... | https://math.stackexchange.com |
1,052,118 | [
"https://math.stackexchange.com/questions/1052118",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/89487/"
] | I know this seems like an obvious question, but I haven't been able to find any examples of sentences in logic higher than second order, so my intuition on how it's supposed to behave is failing me. There are descriptions describing third order logic as 'properties of properties' but without example syntax, I'm not sur... | The axioms of topology, for example, can be seen as third-order axioms. Simply because of the axiom that a topology is closed under unions:
$$\forall\mathcal U((\forall U\in\mathcal U\rightarrow U\in\tau)\rightarrow(\exists V\forall x(x\in V\leftrightarrow\exists U\in\mathcal U(x\in U))\land V\in\tau))$$
In the langu... | In the context of higher-order arithmetic, there are many natural third-order statements. In arithmetic, quantifiers over natural numbers are first-order, quantifiers over sets of natural numbers are second-order, and quantification over sets of sets of natural numbers is third-order.
Using standard coding methods, ... | https://math.stackexchange.com |
92,013 | [
"https://mathoverflow.net/questions/92013",
"https://mathoverflow.net",
"https://mathoverflow.net/users/18589/"
] | For an immersed closed surface $f: \Sigma \rightarrow \mathbb R^3$ the Willmore functional is defined as
$$
\cal W(f) = \int _{\Sigma} \frac{1}{4} |\vec H|^2 d \mu_g,
$$
where $\vec H$ is the mean curvature vector in $\mathbb R^3$and $g$ is the induced metric.
If $\Sigma$ is closed we have the estimate
$$
\cal W(f... | First of all, by a result of Bauer and Kuwert, there exists a smooth minimizer of the Willmore functional in the class of compact surfaces with fixed genus g, for any g. They have Willmore functional below $8\pi$ and by a result of Kuwert, Li and Schaetzle, the Willmore functional of the minimzers for genus $g$ tends t... | I remember there is a paper by Kusner named: comparison surfaces for the Willmore problem in which the author
conjectured that the Lawson surface(see Sebastian's answer) minimizes the Willmore energy of genus g surface. For surfaces immersed in R^n, it is also conjectured the Clifford torus should be the minimizer, bu... | https://mathoverflow.net |
12,047 | [
"https://mechanics.stackexchange.com/questions/12047",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/24/"
] | I own a 1997 golf 3 TDI, motor code AFN.
At the back of the engine, there is a vacuum actuator which looks like a N75 but isn't. It isn't connected to anything on the actuator side, but is connected to the vacuum line and the ECU.
It doesn't seem to have done much to the running, as I cannot detect a difference in po... | I found out what it is. It controls the air recirculation flap to the cabin. Nothing to do with the engine at all.
Just above the input and output pipes to the heater core on the firewall is a little plastic nozzle. This is what this actuator is supposed to be connected to.
| This is more than likely a vacuum switch which tells the computer <em>something</em> when it reaches a certain amount of vacuum (could also be a pressure switch doing the same thing when the turbo reaches a certain pressure, depending on which side of the turbo the "vacuum" line is located). This would be why you are o... | https://mechanics.stackexchange.com |
3,806,472 | [
"https://math.stackexchange.com/questions/3806472",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/544640/"
] | I have successfully derived the equation <span class="math-container">$\sin(y)=\frac{e^{iy}-e^{-iy}}{2i}$</span> and its corresponding cosine partner <span class="math-container">$\cos(y)=\frac{e^{iy}+e^{-iy}}{2}$</span> <strong>where <span class="math-container">$y \in \mathbb R$</span></strong>.
In my book, the gener... | To prove something about <span class="math-container">$\cos(z), \sin(z)$</span> you need first to define <span class="math-container">$\cos(z), \sin(z)$</span>.
The formulas you are trying to prove are the usual definitions.
Alternatelly, you can prove the following result:
<strong>Lemma:</strong> There exists an uniqu... | The usual definition of <span class="math-container">$\sin(z)$</span> and <span class="math-container">$\cos(z)$</span> for <span class="math-container">$z \in \mathbb{C}$</span> is <span class="math-container">$\sin(z)=\frac{e^{i z}-e^{-i z}}{2i}$</span> and <span class="math-container">$\cos(z)=\frac{e^{i z}+e^{-i z}... | https://math.stackexchange.com |
560,938 | [
"https://math.stackexchange.com/questions/560938",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/42267/"
] | Find $\lim_{x\to+\infty}(\sqrt{(x+a_1)(x+a_2)}-x)$
First I rationalized the numerator,
$$
\begin{align*}
&\lim_{x\to+\infty}(\sqrt{(x+a_1)(x+a_2)}-x) \cdot \frac{\sqrt{(x+a_1)(x+a_2)}+x}{\sqrt{(x+a_1)(x+a_2)}+x} \\
=&\lim_{x\to+\infty}\frac{x(a_1+a_2)+a_1a_2}{\sqrt{(x+a_1)(x+a_2)}+x} \\
=&\lim_{x\to+\inft... | You do it right until the last line $\lim_{x\to+\infty}\frac {x(a_1+a_2)+a_1a_2}{\sqrt {(x+a_1)(x+a_2)}+x}=\lim_{x\to+\infty}\frac {x(a_1+a_2)+a_1a_2}{\sqrt {x^2+(a_1+a_2)x+a_1a_2} +x}$=$\lim_{x\to+\infty}\frac {x((a_1+a_2)+a_1a_2x^{-1})}{|x| \left( \sqrt {1+(a_1+a_2)x^{-1}+a_1a_2x^{-2}}+1 \right)} $
For $x>0$ we h... | Putting $h=\frac1x$
$$\lim_{h\to0}\frac{\sqrt{(1+a_1h)(1+a_2h)}-1}h$$
$$=\lim_{h\to0}\frac{(1+a_1h)(1+a_2h)-1}{h\cdot(\sqrt{(1+a_1h)(1+a_2h)}+1)}\text{( rationalizing the numerator)}$$
$$=\lim_{h\to0}\frac{a_1+a_2+a_1a_2h}{\sqrt{(1+a_1h)(1+a_2h)}+1}\text{ as }h\ne0\text{ as }h\to0$$
$$=\frac{a_1+a_2}{\sqrt{(1)(1)}+... | https://math.stackexchange.com |
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